Math Problem Statement

A body of mass 5 kg is at rest on a rough horizontal surface even after the action of various forces as shown in the figure. The frictional force acting on the body is:

Solution

To solve this question, let’s analyze the forces acting on the 5 kg body at rest on a rough horizontal surface:

Given Information:

  • Mass of the body, m=5kgm = 5 \, \text{kg}
  • Forces acting horizontally:
    • 6 N to the left
    • 8 N to the right
    • 4 N to the left
    • 2 N to the right

Solution:

  1. Calculate the Net Horizontal Force:

    • Total force to the right = 8N+2N=10N8 \, \text{N} + 2 \, \text{N} = 10 \, \text{N}
    • Total force to the left = 6N+4N=10N6 \, \text{N} + 4 \, \text{N} = 10 \, \text{N}
    • Since the forces to the left and right are equal, the net horizontal force is zero.
  2. Determine the Frictional Force:

    • Since the body is at rest and the net applied force is zero, there is no unbalanced force trying to move the body.
    • Therefore, the frictional force acting on the body must also be zero to keep it stationary.

Answer:

The correct answer is:

  • A. Zero

Would you like further explanation or details on this?


Related Questions:

  1. What would happen if the force to the right was greater than the force to the left?
  2. How would the frictional force change if the surface were smoother?
  3. What role does the mass of the body play in this scenario?
  4. How can we calculate the coefficient of friction in such problems?
  5. How would this scenario change if the body was accelerating?

Tip:

Remember that frictional force acts to counteract any motion. If there is no net force, friction will be zero on a stationary object.

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Math Problem Analysis

Mathematical Concepts

Forces
Equilibrium
Newton's First Law of Motion

Formulas

Net force = Sum of all forces acting in a direction

Theorems

Newton's First Law of Motion

Suitable Grade Level

Grades 9-10